Neuronal computation on complex dendritic morphologies

When we think about neural cells, we immediately recall the wealth of electrical behaviour which, eventually, brings about consciousness. Hidden deep in the frequencies and timings of action potentials, in subthreshold oscillations, and in the cooperation of tens of billions of neurons, are synchronicities and emergent behaviours that result in high-level, system-wide properties such as thought and cognition. However, neurons are even more remarkable for their elaborate morphologies, unique among biological cells. The principal, and most striking, component of neuronal morphologies is the dendritic tree. Despite comprising the vast majority of the surface area and volume of a neuron, dendrites are often neglected in many neuron models, due to their sheer complexity. The vast array of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of subthreshold dendritic currents. In this thesis, we will explore the properties of neuronal dendritic trees, and how they alter and integrate the electrical signals that diffuse along them. After an introduction to neural cell biology and membrane biophysics, we will review Abbott's dendritic path integral in detail, and derive the theoretical convergence of its infinite sum solution. On certain symmetric structures, closed-form solutions will be found; for arbitrary geometries, we will propose algorithms using various heuristics for constructing the solution, and assess their computational convergences on real neuronal morphologies. We will demonstrate how generating terms for the path integral solution in an order that optimises convergence is non-trivial, and how a computationally-significant number of terms is required for reasonable accuracy. We will, however, derive a highly-efficient and accurate algorithm for application to discretised dendritic trees. Finally, a modular method for constructing a solution in the Laplace domain will be developed

Model and Appearance Based Analysis of Neuronal Morphology from Different Microscopy Imaging Modalities

The neuronal morphology analysis is key for understanding how a brain works. This process requires the neuron imaging system with single-cell resolution; however, there is no feasible system for the human brain. Fortunately, the knowledge can be inferred from the model organism, Drosophila melanogaster, to the human system. This dissertation explores the morphology analysis of Drosophila larvae at single-cell resolution in static images and image sequences, as well as multiple microscopy imaging modalities. Our contributions are on both computational methods for morphology quantification and analysis of the influence of the anatomical aspect. We develop novel model-and-appearance-based methods for morphology quantification and illustrate their significance in three neuroscience studies. Modeling of the structure and dynamics of neuronal circuits creates understanding about how connectivity patterns are formed within a motor circuit and determining whether the connectivity map of neurons can be deduced by estimations of neuronal morphology. To address this problem, we study both boundary-based and centerline-based approaches for neuron reconstruction in static volumes. Neuronal mechanisms are related to the morphology dynamics; so the patterns of neuronal morphology changes are analyzed along with other aspects. In this case, the relationship between neuronal activity and morphology dynamics is explored to analyze locomotion procedures. Our tracking method models the morphology dynamics in the calcium image sequence designed for detecting neuronal activity. It follows the local-to-global design to handle calcium imaging issues and neuronal movement characteristics. Lastly, modeling the link between structural and functional development depicts the correlation between neuron growth and protein interactions. This requires the morphology analysis of different imaging modalities. It can be solved using the part-wise volume segmentation with artificial templates, the standardized representation of neurons. Our method follows the global-to-local approach to solve both part-wise segmentation and registration across modalities. Our methods address common issues in automated morphology analysis from extracting morphological features to tracking neurons, as well as mapping neurons across imaging modalities. The quantitative analysis delivered by our techniques enables a number of new applications and visualizations for advancing the investigation of phenomena in the nervous system

Optical analysis of synaptic plasticity in rat hippocampus

Long-term potentiation (LTP) in the CA1 region of the hippocampus is dependent on NMDA receptor activation. Downstream of NMDA receptor signaling, the activation of α-calcium/calmodulin-dependent protein kinase II (αCaMKII) is both necessary and sufficient for the induction of this form of LTP. It has been shown that αCaMKII accumulates in spines after glutamate application or ‘chemical LTP’. This postsynaptic accumulation of αCaMKII could be a key step for the induction of LTP, because it localizes the activated kinase close to the substrates of synaptic potentiation. It is not clear, however, what the threshold, time course of αCaMKII translocation are, and whether it is specific to the stimulated synapses only. To address these three questions, I combined optical stimulation techniques (Channelrhodopsin-2 stimulation and two-photon glutamate uncaging) with optical measurements of calcium transients and αCaMKII concentration. This ‘all-optical’ approach made it possible to investigate synapse-specific changes during the induction of LTP. I could show that coincident activity of pre- and postsynaptic cells was needed to trigger the translocation of αCaMKII. Functional potentiation could be measured immediately after stimulation, whereas αCaMKII accumulation reached its peak ~10 min later. This points to an additional structural role of αCaMKII at the postsynaptic density. Both αCaMKII fractions, the cytoplasmic fraction and postsynaptic bound αCaMKII, increased after optical LTP induction. These changes were restricted to stimulated spines. In spines that showed a persistent volume increase, the amount of bound αCaMKII was increased by a factor of two after 30-40 minutes. A second very interesting finding was the close correlation between spine volume changes and LTP, in terms of the time course, induction threshold and specificity. The optical LTP protocol led to a lasting volume increase only in the stimulated spines, but not in directly neighboring spines on the same dendrite. Spine volume reached its maximum immediately after stimulation. Since my all-optical approach relied heavily on the use of a newly identified light-gated cation channel (Channelrhodopsin-2, ChR2), I finally also characterized light activation of ChR2 in hippocampal pyramidal cells in detail. Neuronal activity could be controlled by blue light with millisecond precision. No direct activation of ChR2 was observed by two-photon imaging lasers, making it possible to combine the ChR2 stimulation technique with two-photon imaging. This led to a third important finding: the release probability of ChR2-expressing axonal terminals was increased if the action potential was induced by light. As a result, pairing of light stimulation with postsynaptic depolarization induced reliable long-term potentiation at CA1 synapses. In summary, the new all-optical approach that combines ChR2 stimulation, two-photon glutamate uncaging, and optical measurements of calcium transients and protein concentration, provides a new avenue for investigating plasticity at the level of single synapses. The induction of LTP in single synapses revealed that accumulation of αCaMKII is input specific thus validating Hebb’s postulate on a micrometer scale

Automated Reconstruction of Evolving Curvilinear Tree Structures

Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashion is of great value in many different scientific domains. However, it remains an open Computer Vision problem. In this thesis we focus on automatically delineating curvilinear tree structures in images of the same object of interest taken at different time instants. Unlike virtually all of the existing methods approaching the task of tree structures delineation we process all the images at once. This is useful in the more ambiguous regions and allows to reason for the tree structure that fits best to all the acquired data. We propose two methods that utilize this principle of temporal consistency to achieve results of higher quality compared to single time instant methods. The first, simpler method starts by building an overcomplete graph representation of the final solution in all time instants while simultaneously obtaining correspondences between image features across time. We then define an objective function with a temporal consistency prior and reconstruct the structures in all images at once by solving a mathematical optimization. The role of the prior is to encourage solutions where for two consecutive time instants corresponding candidate edges are either both retained or both rejected from the final solution. The second multiple time instant method uses the same overcomplete graph principle but handles the temporal consistency in a more robust way. Instead of focusing on the very local consistency of single edges of the overcomplete graph we propose a method for describing topological relationships. This favors solutions whose connectivity is consistent over time. We show that by making the temporal consistency more global we achieve additional robustness to errors in the initial features matching step, which is shared by both the approaches. In the end, this yields superior performance. Furthermore, an added benefit of both our approaches is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data. We also propose a simple single time instant method for delineating tree structures. It computes a Minimum Spanning Arborescence of an initial overcomplete graph and proceeds to optimally prune spurious branches. This yields results of lower but still competitive quality compared to the mathematical optimization based methods, while keeping low computational complexity. Our methods can applied to both 2D and 3D data. We demonstrate their performance in 3D on microscopy volumes of mouse brain and rat brain. We also test them in 2D on time-lapse images of a growing runner bean and aerial images of a road network

Methods for Automated Neuron Image Analysis

Knowledge of neuronal cell morphology is essential for performing specialized analyses in the endeavor to understand neuron behavior and unravel the underlying principles of brain function. Neurons can be captured with a high level of detail using modern microscopes, but many neuroscientific studies require a more explicit and accessible representation than offered by the resulting images, underscoring the need for digital reconstruction of neuronal morphology from the images into a tree-like graph structure. This thesis proposes new computational methods for automated detection and reconstruction of neurons from fluorescence microscopy images. Specifically, the successive chapters describe and evaluate original solutions to problems such as the detection of landmarks (critical points) of the neuronal tree, complete tracing and reconstruction of the tree, and the detection of regions containing neurons in high-content screens

Molecular dissection of ephrinB reverse signaling

Synapses form when highly motile dendritic filopodia establish axonal contacts. When a synaptic contact is stabilized, it gives rise to the formation of a dendritic spine, which has recently been shown to involve a number of molecules that mostly regulate the actin cytoskeleton. Thus, it is not surprising that Eph receptor tyrosine kinases, as known regulators of signaling pathways involved in actin cytoskeleton remodeling, have been shown to be required for spine development and maintenance. The main characteristic of interactions of the Eph receptor with its membrane associated ephrin ligand is that they can propagate bidirectional signals. Both forward (downstream of Eph receptor) and reverse (downstream of ephrin ligand) signaling have been shown to play a role in mature synapses, where spine morphology changes are associated with synaptic plasticity. Thus, ephrinB reverse signaling might be as important for dendritic spine development as signaling pathways downstream of Eph receptors. Intrigued by this idea, we hypothesized that some of the spine morphology changes during plasticity might be regulated exclusively by ephrin reverse signaling pathways. Analyzing spine formation in cultures of dissociated hippocampal neurons, we demonstrated that stimulation of hippocampal neurons with EphB receptor bodies leads to increased spine maturation. Expression of a truncated form of ephrinB ligand, which is still able to activate EphB receptor but is unable to transduce intracellular signals, impairs spine morphology. To find new players of reverse signaling that are important in directing ephrin-mediated spine morphology, we performed a proteomic analysis of the phosphotyrosine dependent ephrin interactor Grb4 (Nck-2, Nck beta). We identified the signaling adaptor G protein-coupled receptor kinase-interacting protein (GIT)1 (Cat1) as well as the exchange factor for Rac βPIX (β-p21-activated protein kinase (PAK)-interacting exchange factor), also called RhoGEF7 or Cool-1, as novel Grb4 binding partners, which have both previously been shown to be required for spine formation. We show that Grb4 binds and recruits GIT1 to synapses downstream of activated ephrinB ligand. Interactions of Grb4 with ephrin or GIT1 are necessary for proper spine morphogenesis and synapse formation. We therefore provide evidence for an important role of ephrinB reverse signaling in spine formation and describe the ephrinB reverse signaling pathway involved in this process